would the swap from 3.55's to 3.92's be worth the cost? im 4wd so have both diff's to do so pretty much double the cost, already have factory lsd so no extra cost for that, I don't tow too frequently, heaviest thing I tow is a trailer of fire wood a couple times a year, trailer holds about 4-4.5 cords of birch, obviously the added performance is a bonus but is the cost worth it for the bit I tow?
Wood is pretty heavy, if you didn't know a cord of Yellow Birch weighs approximately 5,100lbs , a cord of White Birch is 4,500lbs.
So even if you are getting white birch, fitting in 4 cords your looking at 18,000lbs + your trailer weight. You'd have to have a serious trailer to properly handle that weight. If I had to guess how much the trailer weighed I'd say easily 5,000lbs. Putting you at approximately 23,000lbs.
If you're hauling this with your 2013 Ram 1500 Sport I'm impressed. If you didn't know as per RAM your max payload is 1368lbs and max towing is 8,500lbs. The tongue weight alone on that trailer of yours fully loaded and evenly balanced would be at least 2,070lbs (9% some say that's the safe minimum) Now granted that's actually not to much over from what RAM Says. However, that still leaves you pulling all that weight.
Personally, I wouldn't change the Axle ratio. As per RAM, yet again, if you had the 3.92 your Max Towing only goes up 1,500lbs and your max payload actually goes down by about 30lbs. You are still going to be pulling almost double what your rated to do safely. Then on top of that you loose a few mpg the rest of the year. I would use that money and save it to repair any damages you might see from towing all this. Or even upgrade your brakes. Stopping 23,000lbs can't be fun.
Next time you get a chance stop by a weight station and have them weigh your front and rear axles preferably on a full tank of gas. Then when you are hauling the trailer (empty) include the trailers axles as well. And finally, when the trailer is full include all 3 axles again. That'll tell you how badly your truly stressing your rig. I'm most concerned about your rear axle.
On the inside door frame on the drive side you'll find your max axle loads. Mine are 3,900lbs front and rear. When I recently pulled a trailer over 4,000 miles I was over my Max combined weight rating. 13,756 to my max of 13,500. I was also just shy of 200lbs over my rear axle weight rating. Nothing bad happened during the trip but I was only barely over. I'm curious to know what yours looks like all loaded up.
Sorry for the long response but I hope this helps you decide.
